∵RT△ABD中,G是BD中点
∴AG=DG
∴∠CAD=∠CDA
∴∠AGE=2∠D
∵∠ABE=∠BAD=90°
∴AD∥BE
∴∠ADF=∠BED
∵∠AED=2∠BED
∴∠AED=2∠D
∴AE=AG